Bottlenecked Transformers: Periodic KV Cache Abstraction for Generalised Reasoning

Abstract: Despite their impressive capabilities, LLMs struggle with generalisation beyond their training distribution, often exhibiting sophisticated pattern interpolation rather than true abstract reasoning (extrapolation). In this work, we approach this limitation through the lens of Information Bottleneck (IB) theory, which posits that model generalisation emerges from an optimal balance between input compression and retention of predictive information in latent representations. We prove using IB theory that decoder-only Transformers are inherently constrained in their ability to form task-optimal sequence representations. We then use this result to demonstrate that periodic global transformation of the internal sequence-level representations (KV cache) is a necessary computational step for improving Transformer generalisation in reasoning tasks. Based on these theoretical insights, we propose a modification to the Transformer architecture, in the form of an additional module that globally rewrites the KV cache at periodic intervals, shifting its capacity away from memorising input prefixes and toward encoding features most useful for predicting future tokens. Our model delivers substantial gains on mathematical reasoning benchmarks, outperforming both vanilla Transformers with up to 3.5x more parameters, as well as heuristic-driven pruning mechanisms for cache compression. Our approach can be seen as a principled generalisation of existing KV-cache compression methods; whereas such methods focus solely on compressing input representations, they often do so at the expense of retaining predictive information, and thus their capabilities are inherently bounded by those of an unconstrained model. This establishes a principled framework to manipulate Transformer memory using information theory, addressing fundamental reasoning limitations that scaling alone cannot overcome.